Spin-locality of higher-spin theories and star-product functional classes
O. A. Gelfond, M. A. Vasiliev
Abstract
A bstract The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the β → −∞ limiting shifted homotopy proposed recently in [1] where all ω 2 C 2 higher-spin vertices were shown to be spin-local. For the β → −∞ limiting shifted contracting homotopy we identify the class of functions $$ {\mathcal{H}}^{+0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> </mml:math> , that do not contribute to the r.h.s. of HS field equations at a given order. A number of theorems and relations that organize analysis of the higher-spin equations are derived including extension of the Pfaffian Locality Theorem of [2] to the β -shifted contracting homotopy and the relation underlying locality of the ω 2 C 2 sector of higher-spin equations. Space-time interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is space-time local in terms of original con- stituent fields ϕ and their local currents J ( ϕ ) of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.